The present invention relates to ultra-high speed optical transport systems. The optical communication systems have been rapidly evolving recently in order to meet continuously increasing demands on transmission capacity, originating mostly from the Internet and multimedia applications. In order to satisfy high capacity demands, according to some industry experts, the 1 TbE standards is needed. Coherent optical OFDM is one possible pathway towards achieving beyond 1 Tb/s optical transport. Initial studies, unfortunately, indicate that the system Q-factor when multiband OFDM with orthogonal sub-bands is used is low, about 13.2 dB after 1000 km of SMF, which represents a very tight margin in terms of 7% overhead for RS(255,239) code, unless strong LDPC codes are used. Another approach is based on multidimensional coded modulation. Namely, by increasing the number of dimensions (i.e., the number of orthonormal basis functions), the aggregate data rate of the system can be increased without degrading the bit error rate (BER) performance as long as orthogonality among basis functions is preserved. Conventional approaches on multidimensional signal constellations for optical communications so far have been related to single carrier systems.